IPhO Syllabus
Accepted 2014 in Astana, amended 2015 in Mumbai.
1 Introduction
2.2
1.1 Purpose of this syllabus
2.2.1
Mechanics
Kinematics
Velocity and acceleration of a point particle as the derivaThis syllabus lists topics which may be used for the IPhO.
tives of its displacement vector. Linear speed; centripetal
Guidance about the level of each topic within the syland tangential acceleration. Motion of a point particle
labus is to be found from past IPhO questions.
with a constant acceleration. Addition of velocities and
angular velocities; addition of accelerations without the
1.2 Character of the problems
Coriolis term; recognition of the cases when the Coriolis
acceleration is zero. Motion of a rigid body as a rotaProblems should focus on testing creativity and undertion around an instantaneous centre of rotation; velocistanding of physics rather than testing mathematical virties and accelerations of the material points of rigid rotuosity or speed of working. The proportion of marks altating bodies.
located for mathematical manipulations should be kept
small. In the case of mathematically challenging tasks,
2.2.2 Statics
alternative approximate solutions should receive partial
credit. Problem texts should be concise; the theoreti- Finding the centre of mass of a system via summation
cal and the experimental examination texts should each or via integration. Equilibrium conditions: force balance
contain fewer than 12000 characters (including white (vectorially or in terms of projections), and torque balance (only for one- and two-dimensional geometry). Norspaces, but excluding cover sheets and answer sheets).
mal force, tension force, static and kinetic friction force;
Hooke’s law, stress, strain, and Young modulus. Stable
1.3 Exceptions
and unstable equilibria.
Questions may contain concepts and phenomena not
mentioned in the Syllabus providing that sufficient in- 2.2.3 Dynamics
formation is given in the problem text so that students
Newton’s second law (in vector form and via projections
without previous knowledge of these topics would not
(components)); kinetic energy for translational and rotabe at a noticeable disadvantage. Such new concepts must
tional motions. Potential energy for simple force fields
be closely related to the topics included in the syllabus.
(also as a line integral of the force field). Momentum,
Such new concepts should be explained in terms of topangular momentum, energy and their conservation laws.
ics in the Syllabus.
Mechanical work and power; dissipation due to friction.
Inertial and non-inertial frames of reference: inertial
force, centrifugal force, potential energy in a rotating
1.4 Units
frame. Moment of inertia for simple bodies (ring, disk,
Numerical values are to be given using SI units, or units
sphere, hollow sphere, rod), parallel axis theorem; findofficially accepted for use with the SI.
ing a moment of inertia via integration.
It is assumed that the contestants are familiar with
the phenomena, concepts, and methods listed below, and 2.2.4 Celestial mechanics
are able to apply their knowledge creatively.
Law of gravity, gravitational potential, Kepler’s laws (no
derivation needed for first and third law). Energy of a
2 Theoretical skills
point mass on an elliptical orbit.
2.1 General
2.2.5
Hydrodynamics
The ability to make appropriate approximations, while Pressure, buoyancy, continuity law, the Bernoulli equamodelling real life problems. Recognition and ability to tion. Surface tension and the associated energy, capillary pressure.
exploit symmetry in problems.
2.3 Electromagnetic fields
2.4
Oscillations and waves
2.3.1 Basic concepts
2.4.1
Concepts of charge and current; charge conservation and
Kirchhoff’s current law. Coulomb force; electrostatic
field as a potential field; Kirchhoff’s voltage law. Magnetic B-field; Lorentz force; Ampère’s force; Biot-Savart
law and B-field on the axis of a circular current loop and
for simple symmetric systems like straight wire, circular
loop and long solenoid.
Harmonic oscillations : equation of motion, frequency,
angular frequency and period. Physical pendulum and
its reduced length. Behaviour near unstable equilibria. Exponential decay of damped oscillations; resonance
of sinusoidally forced oscillators: amplitude and phase
shift of steady state oscillations. Free oscillations of LCcircuits; mechano-electrical analogy; positive feedback
as a source of instability; generation of sine waves by
feedback in a LC-resonator.
Single oscillator
2.3.2 Integral forms of Maxwell’s equations
Gauss’ law (for E- and B-fields); Ampère’s law; Faraday’s
law; using these laws for the calculation of fields when
the integrand is almost piece-wise constant. Boundary
conditions for the electric field (or electrostatic potential)
at the surface of conductors and at infinity; concept of
grounded conductors. Superposition principle for electric and magnetic fields; uniqueness of solution to wellposed problems; method of image charges.
2.4.2
Waves
Propagation of harmonic waves: phase as a linear function of space and time; wave length, wave vector, phase
and group velocities; exponential decay for waves propagating in dissipative media; transverse and longitudinal
waves; the classical Doppler effect. Waves in inhomogeneous media: Fermat’s principle, Snell’s law. Sound
waves: speed as a function of pressure (Young’s or bulk
modulus) and density, Mach cone. Energy carried by
waves: proportionality to the square of the amplitude,
2.3.3 Interaction of matter with electric and magnetic
continuity of the energy flux.
fields
Resistivity and conductivity; differential form of Ohm’s
law. Dielectric and magnetic permeability; relative permittivity and permeability of electric and magnetic materials; energy density of electric and magnetic fields; ferromagnetic materials; hysteresis and dissipation; eddy
currents; Lenz’s law. Charges in magnetic field: helicoidal motion, cyclotron frequency, drift in crossed Eand B-fields. Energy of a magnetic dipole in a magnetic
field; dipole moment of a current loop.
2.4.3
Interference and diffraction
Superposition of waves: coherence, beats, standing
waves, Huygens’ principle , interference due to thin
films (conditions for intensity minima and maxima only).
Diffraction from one and two slits, diffraction grating,
Bragg reflection.
2.4.4
Interaction of electromagnetic waves with matter
Dependence of electric permittivity on frequency (qualitatively); refractive index; dispersion and dissipation of
Linear resistors and Ohm’s law; Joule’s law; work done electromagnetic waves in transparent and opaque maby an electromotive force; ideal and non-ideal batter- terials. Linear polarisation; Brewster angle; polarisers;
ies, constant current sources, ammeters, voltmeters and Malus’ law.
ohmmeters. Nonlinear elements of given V -I characteristic. Capacitors and capacitance (also for a single
2.4.5 Geometrical optics and photometry
electrode with respect to infinity); self-induction and inductance; energy of capacitors and inductors; mutual in- Approximation of geometrical optics: rays and optical
ductance; time constants for RL and RC circuits. AC images; a partial shadow and full shadow. Thin lens apcircuits: complex amplitude; impedance of resistors, in- proximation; construction of images created by ideal thin
ductors, capacitors, and combination circuits; phasor di- lenses; thin lens equation . Luminous flux and its contiagrams; current and voltage resonance; active power.
nuity; illuminance; luminous intensity.
2.3.4 Circuits
and gas constant; translational motion of molecules and
pressure; ideal gas law; translational, rotational and osTelescopes and microscopes: magnification and resolvcillatory degrees of freedom; equipartition theorem; ining power; diffraction grating and its resolving power;
ternal energy of ideal gases; root-mean-square speed of
interferometers.
molecules. Isothermal, isobaric, isochoric, and adiabatic
processes; specific heat for isobaric and isochoric pro2.5 Relativity
cesses; forward and reverse Carnot cycle on ideal gas and
Principle of relativity and Lorentz transformations for its efficiency; efficiency of non-ideal heat engines.
the time and spatial coordinate, and for the energy and
momentum; mass-energy equivalence; invariance of the
2.7.2 Heat transfer and phase transitions
spacetime interval and of the rest mass. Addition of parallel velocities; time dilation; length contraction; relativ- Phase transitions (boiling, evaporation, melting, subliity of simultaneity; energy and momentum of photons mation) and latent heat; saturated vapour pressure, reland relativistic Doppler effect; relativistic equation of ative humidity; boiling; Dalton’s law; concept of heat
motion; conservation of energy and momentum for elas- conductivity; continuity of heat flux.
tic and non-elastic interaction of particles.
2.4.6 Optical devices
2.6 Quantum Physics
2.7.3
Statistical physics
Planck’s law (explained qualitatively, does not need to
be remembered), Wien’s displacement law; the StefanParticles as waves: relationship between the frequency
Boltzmann law.
and energy, and between the wave vector and momentum.
energy levels of hydrogen-like atoms (circular
orbits only) and of parabolic potentials; quantization of
3 Experimental skills
angular momentum. Uncertainty principle for the conjugate pairs of time and energy, and of coordinate and
3.1 Introduction
momentum (as a theorem, and as a tool for estimates);
2.6.1 Probability waves
The theoretical knowledge required for carrying out the
experiments must be covered by Section 2 of this SylEmission and absorption spectra for hydrogen-like atoms labus.
The experimental problems should contain at least
(for other atoms — qualitatively), and for molecules due
some
tasks for which the experimental procedure (setup,
to molecular oscillations; spectral width and lifetime of
excited states. Pauli exclusion principle for Fermi parti- the list of all the quantities subject to direct measurecles. Particles (knowledge of charge and spin): electrons, ments, and formulae to be used for calculations) is not
electron neutrinos, protons, neutrons, photons; Comp- described in full detail.
2.6.2 Structure of matter
ton scattering. Protons and neutrons as compound particles. Atomic nuclei, energy levels of nuclei (qualitatively); alpha-, beta- and gamma-decays; fission, fusion
and neutron capture; mass defect; half life and exponential decay. photoelectric effect.
2.7 Thermodynamics and statistical physics
2.7.1 Classical thermodynamics
Concepts of thermal equilibrium and reversible processes; internal energy, work and heat; Kelvin’s temperature scale; entropy; open, closed, isolated systems;
first and second laws of thermodynamics. Kinetic theory of ideal gases: Avogadro number, Boltzmann factor
The experimental problems may contain implicit theoretical tasks (deriving formulae necessary for calculations); there should be no explicit theoretical tasks unless
these tasks test the understanding of the operation principles of the given experimental setup or of the physics
of the phenomena to be studied, and do not involve long
mathematical calculations.
The expected number of direct measurements and
the volume of numerical calculations should not be so
large as to consume a major part of the allotted time:
the exam should test experimental creativity, rather than
the speed with which the students can perform technical
tasks.
The students should have the following skills.
3.2 Safety
repeated measurements.
Finding absolute and relative uncertainties of a quanKnowing standard safety rules in laboratory work. Nevtity determined as a function of measured quantities usertheless, if the experimental set-up contains any safety
ing any reasonable method (such as linear approximahazards, the appropriate warnings should be included in
tion, addition by modulus or Pythagorean addition).
the text of the problem. Experiments with major safety
hazards should be avoided.
3.6
3.3 Measurement techniques and apparatus
Being familiar with the most common experimental techniques for measuring physical quantities mentioned in
the theoretical part.
Knowing commonly used simple laboratory instruments and digital and analog versions of simple devices, such as calipers, the Vernier scale, stopwatches, thermometers, multimeters (including ohmmeters and AC/DC voltmeters and ammeters), potentiometers, diodes, , lenses, prisms, optical stands, calorimeters,
and so on.
Sophisticated practical equipment likely to be unfamiliar to the students should not dominate a problem. In
the case of moderately sophisticated equipment (such as
oscilloscopes, counters, ratemeters, signal and function
generators, photogates, etc), instructions must be given
to the students.
3.4 Accuracy
Being aware that instruments may affect the outcome of
experiments.
Being familiar with basic techniques for increasing
experimental accuracy (e.g. measuring many periods instead of a single one, minimizing the influence of noise,
etc).
Knowing that if a functional dependence of a physical quantity is to be determined, the density of taken data
points should correspond to the local characteristic scale
of that functional dependence.
Expressing the final results and experimental uncertainties with a reasonable number of significant digits,
and rounding off correctly.
3.5 Experimental uncertainty analysis
Identification of dominant error sources, and reasonable
estimation of the magnitudes of the experimental uncertainties of direct measurements (using rules from documentation, if provided).
Distinguishing between random and systematic errors; being able to estimate and reduce the former via
Data analysis
Transformation of a dependence to a linear form by appropriate choice of variables and fitting a straight line to
experimental points. Finding the linear regression parameters (gradient, intercept and uncertainty estimate)
either graphically, or using the statistical functions of a
calculator (either method acceptable).
Selecting optimal scales for graphs and plotting data
points with error bars.
4 Mathematics
4.1
Algebra
Simplification of formulae by factorisation and expansion. Solving linear systems of equations. Solving equations and systems of equations leading to quadratic and
biquadratic equations; selection of physically meaningful solutions. Summation of arithmetic and geometric
series.
4.2
Functions
Basic properties of trigonometric, inverse-trigonometric,
exponential and logarithmic functions and polynomials.
This includes formulae regarding trigonometric functions of a sum of angles, Solving simple equations involving trigonometric, inverse-trigonometric, logarithmic and exponential functions.
4.3
Geometry and stereometry
Degrees and radians as alternative measures of angles.
Equality of alternate interior and exterior angles, equality of corresponding angles. Recognition of similar triangles. Areas of triangles, trapezoids, circles and ellipses;
surface areas of spheres, cylinders and cones; volumes
of spheres, cones, cylinders and prisms. Sine and cosine
rules, property of inscribed and central angles, Thales’
theorem, medians and the centroid of a triangle. Students are expected to be familiar with the properties of
conic sections including circles, ellipses, parabolae and
hyperbolae.
4.4 Vectors
4.7
Calculus
Finding derivatives of elementary functions, their sums,
products, quotients, and nested functions. Integration
as the inverse procedure to differentiation. Finding definite and indefinite integrals in simple cases: elementary
functions, sums of functions, and using the substitution
rule for a linearly dependent argument. Making definite
4.5 Complex numbers
integrals dimensionless by substitution. Geometric interpretation of derivatives and integrals. Finding constants
Summation, multiplication and division of complex
of integration using initial conditions. Concept of gradinumbers; separation of real and imaginary parts. Conent vectors (partial derivative formalism is not needed).
version between algebraic, trigonometric, and exponential representations of a complex number. Complex roots
of quadratic equations and their physical interpretation. 4.8 Approximate and numerical methods
Basic properties of vectorial sums, dot and cross products. Double cross product and scalar triple product. Geometrical interpretation of a time derivative of a vector
quantity.
Using linear and polynomial approximations based on
Taylor series. Linearization of equations and expressions.
4.6 Statistics
Perturbation method: calculation of corrections based on
Calculation of probabilities as the ratio of the number of unperturbed solutions. Finding approximate numerical
objects or event occurrence frequencies. Calculation of solutions to equations using, e.g., Newton’s method or
mean values, standard deviations, and standard devia- bisection of intervals. Numerical integration using the
tion of group means.
trapezoidal rule or adding rectangles.